Respuesta :
Given the equation:
[tex]\frac{1}{2}x\text{ - }\frac{3}{4}y\text{ = 6}[/tex]Let's determine the x coordinate of the x-intercept of the line.
[tex]\frac{1}{2}x\text{ - }\frac{3}{4}y\text{ = 6 }\rightarrow\text{ }\frac{3}{4}y\text{ = }\frac{1}{2}x\text{ - 6 }\rightarrow\text{ y = (}\frac{4}{3})(\frac{1}{2}x\text{ - 6)}[/tex][tex]\text{ y = }\frac{4}{6}x\text{ - }\frac{24}{3}\text{ }\rightarrow\text{ y = }\frac{2}{3}x\text{ - 8}[/tex]The x-intercept is therefore, at y = 0:
[tex]\text{ 0 = }\frac{2}{3}x-8\rightarrow\frac{2}{3}x=8\text{ }[/tex][tex]x\text{ = }\frac{3}{2}(8)\text{ }\rightarrow\text{ x = }\frac{24}{2}[/tex][tex]\text{ x = }12[/tex]Therefore, the x coordinate of the x-intercept of the line of the equation is 12.
